Section 9.1 Graphs of Rational Functions and Reducing Rational Expressions

9.1 Lecture Guide: Graphs of Rational Functions and Reducing Rational Expressions Objective 1: Identify rational functions. AlgebraicallyVerbally Algebraic Example is a rational function if and are _______________ and A rational function is defined as the ____________ of two polynomials. Rational Function

Determine whether each function defines a rational function. 1.2.

Determine whether each function defines a rational function

Determine whether each function defines a rational function

Objective 2: Determine the domain and identify the vertical asymptotes of a rational function.

The domain of a rational function must exclude values that would cause ______________ by zero. Algebraic Example Numerical Example Graphical Example Verbal Example The domain of is Only zero is excluded from the domain to prevent division by zero. Note that 1 divided by 0 is undefined. Also note that there is a break in the graph at Domain of a Rational Function

Characteristics of the graph of The domain of this function does not include __________. The function is discontinuous. There is a _________ in the graph at The graph consists of two unconnected The graph approaches the ________________________ asymptotically. The graph approaches the _________________________ asymptotically. line branches.

7. If, evaluate each expression. (a) (b) (c)

8. Given the rational function (a) What value is excluded from the domain of this function? (b) What is the domain of this function? (d) What is the equation of the vertical asymptote of this function?

Determine the domain of each rational function. 9.

Determine the domain of each rational function. 10.

Determine the domain of each rational function. 11.

Determine the domain of each rational function. 12.

13. Use the given table to determine the domain and vertical asymptotes of (a)Domain: (b) Vertical Asymptotes:

14. Use the given graph to determine the domain and vertical asymptotes of (a)Domain: (b) Vertical Asymptotes:

Objective 3: Reduce a rational expression to lowest terms. AlgebraicallyVerbally Algebraic Example If A,B and C are polynomials and and then 1._______________ both the numerator and the denominator of the rational expression. 2.Divide the numerator and the denominator by any common nonzero _____________. Reducing a Rational Expression to Lowest Terms

15. Reduce each rational expression.

16. Reduce each rational expression.

17. Reduce each rational expression.

18. Reduce each rational expression.

19. Reduce each rational expression.

20. Reduce each rational expression.

21. Reduce each rational expression.

22. Reduce each rational expression.

Jerseys Average Cost Per Jersey ($) 23. The average cost per jersey for a screen printer to produce x sports jerseys is displayed in this graph. (a) Describe what happens to the average cost per jersey as the number of jerseys produced becomes very small.

Jerseys Average Cost Per Jersey ($) 23. The average cost per jersey for a screen printer to produce x sports jerseys is displayed in this graph. (b) Describe what happens to the average cost per jersey as the number of jerseys produced becomes very large.

Fill in the missing numerator or denominator. 24.

Fill in the missing numerator or denominator. 25.